Isomorphism between Systems of Equivariant Singularities

In this article isomorphisms between systems of singularities equivariant under different Lie group actions are investigated and a sufficient condition for two systems to be isomorphic is given. With this sufficiency theorem we show that the system ofO(n)-equivariant singularities in its irreducible representation on Rⁿis isomorphic to that of one-dimensional Z₂-equivariant singularities and the system of[formula]-dimensionalO(n)-equivariant singularities is isomorphic to that ofn-dimensionalS_n-equivariant singularities.